Material removal critical grinding force calculation method based on variational mode model

Abstract

The invention relates to the technical field of metal material grinding machining, in particular to a material removal critical grinding force calculation method based on a variational mode model. The method comprises the steps that firstly, grinding force signals are collected, tangential components are extracted, and tangential grinding force data at equal sampling intervals are obtained through sampling detection and interpolation resampling; then, variational mode decomposition parameters are determined, and the signals are decomposed to obtain an intrinsic mode function; the power spectrum density and the center frequency of each mode are calculated through frequency domain analysis, the modes higher than a median value are superposed to form a high-frequency reconstruction signal, and the critical time point of elastic, plastic and brittle transition of the material and the corresponding critical grinding force are determined by combining energy analysis. According to the method, the critical grinding force of the metal material from plastic removal to brittle fracture can be accurately recognized, high-precision critical transformation recognition and efficient signal decomposition and reconstruction are achieved, the problem that plastic-brittle transformation is difficult to recognize in existing grinding machining is solved, and the machining quality and the surface integrity are improved.

Description

Technical Field

[0001] This invention belongs to the field of metal material grinding technology, specifically relating to a method for calculating the critical grinding force for material removal based on a variational mode model. Background Technology

[0002] Metallic materials are widely used in aerospace, automotive manufacturing, mold making, and precision engineering, and their processing quality directly affects the service performance and reliability of components. Grinding, as one of the main methods for precision and ultra-precision machining of metallic materials, has irreplaceable advantages in ensuring dimensional accuracy and surface quality. However, due to the typical high temperature, high strain rate, and strong contact coupling characteristics of the grinding process, severe abrasive grain adhesion easily occurs between the grinding wheel and the workpiece. At the same time, because the grinding arc space is narrow, coolant cannot fully enter, limiting effective cooling and lubrication, resulting in a significant increase in grinding temperature and grinding force.

[0003] During this process, residual tensile stress, microcracks, and potential damage easily appear on the surface of metallic materials, leading to surface quality deterioration and becoming potential fatigue sources for components, significantly affecting their fatigue life and service reliability. The removal of metallic materials during grinding mainly manifests in two modes: plastic cutting and brittle fracture. When the abrasive force is below a certain critical value, the material is removed in the form of plastic flow, resulting in high surface integrity; however, when the grinding force exceeds this critical value, the material undergoes brittle fracture, easily forming surface damage such as microcracks and pitting. Therefore, accurately determining the critical grinding force at which metallic materials transition from plastic removal to brittle fracture during grinding is of great significance for achieving high-quality, low-damage machining.

[0004] However, the brittle-plastic transition process is typically abrupt and nonlinear, with extremely short transition phases and indistinct signal characteristics. Traditional identification methods based on force signals or surface morphology struggle to accurately capture this critical state, leading to significant errors in the calculation of the critical grinding force. Therefore, there is an urgent need for an analytical method capable of effectively decomposing and extracting key feature parameters from complex non-stationary signals and accurately identifying the critical grinding force for material removal, in order to achieve precise characterization and control of the grinding behavior of metallic materials. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method for calculating the critical grinding force for material removal based on a variational mode model. By introducing a variational mode decomposition model, the critical grinding force for the ductile-brittle transition during the grinding process of metal materials can be accurately calculated, thereby solving the problem that the ductile-brittle transition point is difficult to accurately identify in the existing technology. This provides reliable technical support for optimizing grinding process parameters, improving processing quality and surface integrity.

[0006] To achieve the above objectives, the technical solution adopted by this invention is a method for calculating the critical grinding force for material removal based on a variational mode model, comprising the following steps: Step 1: Collect grinding force signals during the metal variable cutting deep grinding process, extract the tangential grinding force signal from the grinding force signal, establish the original tangential grinding force data sample, and extract the time data and corresponding tangential grinding force data from the original tangential grinding force data sample; Step 2: Perform sampling interval detection on the extracted time data to determine the uniformity of the time interval. If it is uniform, establish an equal sampling interval tangential grinding force data sample by combining the time data in the original tangential grinding force data sample with the corresponding tangential grinding force data. If it is non-uniform, construct equal interval time data and perform linear interpolation resampling on the tangential grinding force data. Then, establish an equal sampling interval tangential grinding force data sample by combining the equal interval time data with the resampled tangential grinding force data. Step 3: Determine the parameters of the variational mode decomposition of the tangential grinding force by using tangential grinding force data samples with equal sampling intervals; Step 4: Introduce the determined variational mode decomposition parameters of the tangential grinding force into the variational mode model, use the variational mode model to decompose the tangential grinding force data samples with equal sampling intervals, obtain mutually independent intrinsic mode functions through iterative optimization, and save the mutually independent intrinsic mode functions in time series order to form a mode function sample set; Step 5: Perform frequency domain analysis on the independent intrinsic mode functions in the modal function sample set, calculate their spectrum function using fast Fourier transform, and construct the power spectral density function in the form of the square of the amplitude of the spectrum function. Based on the distribution of the power spectral density function, calculate the center frequency of the independent intrinsic mode function using the power weighted average method, and establish a center frequency set for each center frequency. Step 6: Based on the center frequency set, obtain the median value, and classify the eigenmode functions with center frequencies greater than the median value into the high-frequency mode set. Superimpose the high-frequency mode sets to obtain the high-frequency reconstructed signal. Step 7: After obtaining the high-frequency reconstructed signal, perform energy analysis on the high-frequency reconstructed signal and the original tangential grinding force data sample respectively, and calculate the energy distribution of the two in the entire time series; by comparing the proportion of the energy of the high-frequency reconstructed signal to the total energy of the original tangential grinding force data sample, determine the energy ratio of the high-frequency reconstructed signal; the peak point of the energy ratio of the high-frequency reconstructed signal is the critical time point of the elastic-plastic-brittle transition characteristics of the metal material being ground, and the grinding force corresponding to the critical time point is the critical grinding force for the elastic-plastic-brittle transition.

[0007] Furthermore, the grinding force signal collected in step one during the metal variable cutting depth grinding process is selected from the grinding force signal data obtained by a benchtop force gauge during the time period from 1 second after the grinding wheel enters the tool to 1 second before it retracts the tool, in order to ensure the stability of the data. Furthermore, the original tangential grinding force data sample established in step one is an image of the tangential grinding force signal extracted from the overall grinding process monitoring data. This image serves as the original tangential grinding force data sample. Time data and corresponding tangential grinding force data are extracted from this original tangential grinding force data sample, which can be represented as:

[0008]

[0009] In the formula, D This is a sample of the original tangential grinding force data. t i It is a time series. F i For the corresponding original tangential grinding force data, t For the extracted time data, x ( t ) represents the corresponding tangential grinding force data.

[0010] Furthermore, the method for determining the uniformity of the time intervals in step two, which involves sampling interval detection of the extracted time data, is expressed as follows:

[0011] , In the formula, Δ t For time step, median The median. std Standard deviation, mean The value is the average. If the condition is met, it indicates that the extracted time data is uniform; if the condition is not met, it indicates that the extracted time data is not uniform. If the extracted time data is uneven, the constructed equally spaced time data is as follows:

[0012] In the formula, t j For data with equal time intervals, Δ t For time step; Then, linear interpolation resampling is performed on the tangential grinding force data to calculate the resampled tangential grinding force data corresponding to equal time intervals:

[0013]

[0014] In the formula, x k For tangential grinding force data, y j This is the resampled tangential grinding force data.

[0015] Furthermore, the parameters for the variational mode decomposition of the tangential grinding force in step three include the penalty factor α, the quadratic penalty term τ, the number of decomposition modes K, and the DC component flag. DC The initialization method (init) and the convergence threshold (tol) are used; the selection rules for these parameters are as follows: (1) The penalty factor α is used to control the modal bandwidth. Its value is determined according to the smoothness of the grinding signal and the noise level. When the signal noise is large or the characteristic frequency band is wide, α takes a larger value (1000 - 5000) to enhance the smoothness of the components; when the signal fluctuation is small or the frequency band is narrow, α takes a smaller value (100 - 800) to preserve details. (2) The second-order penalty term τ is the time step of the Lagrange multiplier update, which is generally zero or a small positive number to ensure stable convergence of the algorithm; (3) The number of decomposed modes K is determined based on the signal complexity and the number of main frequency bands. It is usually between 3 and 8. For grinding force signals, it is preferred to be 5 in order to balance the modal resolution and computational complexity. (4) DC component marking DC Determine whether to include a zero-frequency mode; set to 1 if the signal contains a stable baseline component, otherwise set to 0. (5) Initialization method init represents the initial center frequency setting method. It is preferred to use uniform distribution initialization init=1 to avoid getting trapped in local optima; (6) The convergence threshold tol controls the decomposition accuracy, with a value range of 10. -5 -10 -8 Convergence is determined when the change in mode between adjacent iterations is less than this threshold.

[0016] Furthermore, the expression for decomposing the tangential grinding force data samples with equal sampling intervals using a variational modal model in step four is as follows:

[0017] In the formula, u k ( t ) is the first K One modal component, w k For the first K One central angular frequency, For the Dirac function, For convolution operators, For L2 norm operations, s . t . represents the constraint condition. y j For resampled tangential grinding force data; Furthermore, the iterative optimization yields K The independent intrinsic mode functions are stored in time series order as IMF1, IMF2, ..., IMF K The modal function sample set is represented as follows:

[0018] In the formula, IMF for K A number of independent eigenmode functions K It is a time series.

[0019] Furthermore, in step five, the process of performing frequency domain analysis on the independent intrinsic mode functions in the mode function sample set and calculating their spectrum functions using Fast Fourier Transform is as follows:

[0020] In the formula, f For frequency variables, U k ( f ) is the first k The complex spectrum of each modal component u k ( t ) is the first K One modal component; The power spectral density function is constructed using the square of the amplitude of the spectral function. The process is as follows:

[0021] In the formula, Pk ( f ) is the power spectral density function. Uk ( f ) represents the complex spectrum of the k-th modal component; Based on the distribution of the power spectral density function, the center frequencies of the independent eigenmode functions are calculated using the power-weighted average method. The process is as follows:

[0022] In the formula, f c,k For the first k The center frequency of each mode; This represents summation over all frequency points; P k ( f) is the power spectral density function.

[0023] Furthermore, the high-frequency reconstruction signal in step six is:

[0024] In the formula, xhigh ( t () is a high-frequency reconstructed signal. UK ( t ) is the first K One modal component.

[0025] Furthermore, the calculation method for the high-frequency reconstructed signal energy ratio in step seven includes the following steps: First, the total energy of the original tangential grinding force data sample in the time domain is calculated to characterize the energy distribution of the entire signal over the time series. The calculation method is as follows:

[0026] In the formula, Etotal This represents the total energy of the original tangential grinding force data sample. x ( t This represents the original tangential grinding force signal; Secondly, the energy of the high-frequency reconstructed signal is calculated to characterize the energy distribution of the signal in the high-frequency subspace. The calculation method is as follows:

[0027] In the formula, Ehigh The energy of the high-frequency reconstructed signal, xhigh ( t () is a high-frequency reconstructed signal; Finally, to achieve time-series characterization of high-frequency energy, the local energy ratio of the signal is calculated using the sliding window method to obtain the energy ratio of the high-frequency reconstructed signal:

[0028] In the formula, R ( i () indicates the center time of the window. i The high-frequency energy ratio at that location L The sliding window length controls the smoothness of the time-domain energy estimation; the numerator represents the time-domain integral of the high-frequency component energy within the window, and the denominator represents the time-domain integral of the total energy within the same window.

[0029] The beneficial effects of this invention are as follows: This invention provides a method for calculating the critical grinding force for material removal based on variational modal model. It utilizes variational modal decomposition (VMD) to adaptively decompose the original grinding force signal, effectively extracting characteristic modal components related to the ductile-brittle transition. This allows for accurate identification of the critical normal grinding force and corresponding tangential grinding force at which the metal material transitions from ductile removal to brittle fracture, overcoming the shortcomings of traditional methods that struggle to accurately determine the transition point when directly analyzing the original signal or surface morphology. Furthermore, this invention, through the adaptive characteristics of the VMD algorithm, effectively decomposes the complex original grinding force signal into independent intrinsic mode functions, distinguishing characteristic signals in different frequency bands, and accurately extracting key modal parameters through energy characteristics and time-frequency distribution analysis. This process avoids noise interference, improves the accuracy of signal separation and reconstruction, and provides a reliable basis for subsequent critical grinding force calculation. This method can accurately calculate the critical grinding force at which the metal material transitions from ductile removal to brittle fracture during grinding, achieving stable removal of the material in the ductile domain and improving the surface quality and machining accuracy of the workpiece. Attached Figure Description

[0030] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the tangential grinding force collected by the present invention; Figure 3 This is a schematic diagram illustrating the decomposition of the tangential grinding force signal into intrinsic mode function signals according to the present invention; Figure 4 This is a schematic diagram illustrating the center frequency calculation of the present invention; Figure 5 This is a schematic diagram of the high-frequency reconstructed signal of the present invention; Figure 6 This is a schematic diagram of the high-frequency energy ratio calculation results of the present invention. Detailed Implementation

[0031] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0032] To achieve the above objectives, the present invention provides the following specific embodiments: Example 1: As Figure 1 As shown, a method for calculating the critical grinding force for material removal based on a variational mode model includes the following steps: Step 1: Collect grinding force signals during the metal variable cutting deep grinding process, extract the tangential grinding force signal from the grinding force signal, establish the original tangential grinding force data sample, and extract the time data and corresponding tangential grinding force data from the original tangential grinding force data sample; The grinding force signal collected during the metal variable cutting deep grinding process is selected from the grinding force signal data obtained by a benchtop force gauge during the time period from 1 second after the grinding wheel enters the tool to 1 second before it retracts the tool, in order to ensure the stability of the data. The established original tangential grinding force data sample is a tangential grinding force signal image extracted from the overall grinding process monitoring data. This original tangential grinding force data sample is used to extract time data and corresponding tangential grinding force data, which can be represented as follows:

[0033]

[0034] In the formula, D This is a sample of the original tangential grinding force data. t i It is a time series. F i For the corresponding original tangential grinding force data, t For the extracted time data, x ( t ) represents the corresponding tangential grinding force data.

[0035] Step 2: Perform sampling interval detection on the extracted time data to determine the uniformity of the time interval. If it is uniform, establish an equal sampling interval tangential grinding force data sample by combining the time data in the original tangential grinding force data sample with the corresponding tangential grinding force data. If it is non-uniform, construct equal interval time data and perform linear interpolation resampling on the tangential grinding force data. Then, establish an equal sampling interval tangential grinding force data sample by combining the equal interval time data with the resampled tangential grinding force data. Step 3: Determine the parameters of the variational mode decomposition of the tangential grinding force by using tangential grinding force data samples with equal sampling intervals; Step 4: Introduce the determined variational mode decomposition parameters of the tangential grinding force into the variational mode model, use the variational mode model to decompose the tangential grinding force data samples with equal sampling intervals, obtain mutually independent intrinsic mode functions through iterative optimization, and save the mutually independent intrinsic mode functions in time series order to form a mode function sample set; Step 5: Perform frequency domain analysis on the independent intrinsic mode functions in the modal function sample set, calculate their spectrum function using fast Fourier transform, and construct the power spectral density function in the form of the square of the amplitude of the spectrum function. Based on the distribution of the power spectral density function, calculate the center frequency of the independent intrinsic mode function using the power weighted average method, and establish a center frequency set for each center frequency. Step 6: Based on the center frequency set, obtain the median value, and classify the eigenmode functions with center frequencies greater than the median value into the high-frequency mode set. Superimpose the high-frequency mode sets to obtain the high-frequency reconstructed signal. Step 7: After obtaining the high-frequency reconstructed signal, perform energy analysis on the high-frequency reconstructed signal and the original tangential grinding force data sample respectively, and calculate the energy distribution of the two in the entire time series; by comparing the proportion of the energy of the high-frequency reconstructed signal to the total energy of the original tangential grinding force data sample, determine the energy ratio of the high-frequency reconstructed signal; the peak point of the energy ratio of the high-frequency reconstructed signal is the critical time point of the elastic-plastic-brittle transition characteristics of the metal material being ground, and the grinding force corresponding to the critical time point is the critical grinding force for the elastic-plastic-brittle transition.

[0036] Specific application examples of the present invention are as follows: The material removal critical grinding force calculation method based on the variational mode model is specifically applied as follows: using diamond abrasive grains with a diameter of 40 μm and a cutting edge height of 80 μm, a titanium-aluminum alloy workpiece with a size of 20×20×10 mm is ground with a single abrasive grain. The grinding speed is 500 mm / min, the variable depth of cut is 0-13 μm, and the grinding time is 8 s.

[0037] Step 1: Collect grinding force signals during the variable-cut deep grinding process of titanium-aluminum alloy, extract the tangential grinding force signal from the grinding force signal, establish the original tangential grinding force data sample, and extract the time dataset and the corresponding tangential grinding force dataset from the original tangential force data sample, as follows:

[0038]

[0039] In the formula, D represents the original tangential grinding force data sample. t i It is a time series. F i Here, t represents the corresponding tangential force data, and t represents the extracted grinding time set. x ( t () represents the extracted tangential grinding force dataset.

[0040] Step 2: Perform sampling interval detection on the extracted time dataset to determine the uniformity of its time intervals. The method is as follows:

[0041]

[0042] In the formula, Δ t For time step, median The median. stdStandard deviation, mean The value is the average. If the condition is met, it indicates that the extracted time data is uniform; if the condition is not met, it indicates that the extracted time data is not uniform.

[0043] The time intervals in the extracted time dataset from the experimental example are not uniform. Therefore, equally spaced time data is constructed, and linear interpolation resampling is performed on the tangential grinding force data. The equally spaced time data and the resampled tangential grinding force data are then combined to establish equally sampled tangential grinding force data samples. The specific expression is as follows:

[0044]

[0045] In the formula, y j This is the resampled tangential grinding force data.

[0046] Step 3: The parameters for the variational mode decomposition of the tangential grinding force determined in the experimental example are as follows: (1) The penalty factor α is used to control the modal bandwidth. Its value is determined according to the smoothness of the grinding signal and the noise level. In the example, when the signal characteristic frequency band is wide, α is taken as 2000 to enhance the smoothness of the components. (2) The second-order penalty term τ is the time step of the Lagrange multiplier update. In this example, it is set to zero to ensure that the algorithm converges stably. (3) The number of decomposed modes K is determined based on the signal complexity and the number of main frequency bands. In this example, it is set to 5 in order to balance the modal resolution and computational complexity. (4) DC component marking DC To determine whether to include a zero-frequency mode, the example signal does not contain a stable baseline component, so it is set to 0; (5) The initialization method init represents the initial center frequency setting method. In this embodiment, uniform distribution initialization init=1 is preferred to avoid getting trapped in local optima; (6) The convergence threshold tol controls the decomposition accuracy; in this example, it is set to 10. -7 Convergence is determined when the change in mode between adjacent iterations is less than this threshold.

[0047] Step 4: Introduce the determined variational mode decomposition parameters into the variational mode model, and use the model to decompose the tangential grinding force data samples with equal sampling intervals. The process is as follows:

[0048] In the formula, u k ( t ) is the first K One modal component, w kFor the first K One central angular frequency, For the Dirac function, For convolution operators, For L2 norm operations, s . t . represents the constraint condition. Y j This is the resampled tangential grinding force data.

[0049] The example obtains five independent intrinsic mode functions through iterative optimization, such as... Figure 3 As shown, the modal function samples are saved in time series order as IMF1, IMF2, ..., IMF5, forming an independent set of modal function samples, which can be represented as:

[0050] In the formula, IMF for 5 A number of independent eigenmode functions 5 It is a time series.

[0051] Step 5: Perform frequency domain analysis on each eigenmode function in the modal function sample set, and calculate its spectrum function using Fast Fourier Transform. The specific expression is as follows:

[0052] In the formula, f For frequency variables, U k ( f ) is the first k The complex spectrum of each modal component u k ( t ) is the first k One modal component.

[0053] Furthermore, the power spectral density function is constructed using the square of the amplitude of the spectral function, with the specific expression as follows:

[0054] In the formula, Pk(f) is the power spectral density function. U k ( f ) is the first k The complex spectrum of each modal component.

[0055] Based on the distribution of the power spectral density function, the center frequency of each eigenmode function is calculated using the power weighted average method. The process is as follows:

[0056] In the formula, fc,k For the first k The center frequency of each mode; This represents summation over all frequency points; P k ( f ) is the power spectral density function.

[0057] Finally, a center frequency set is established for each center frequency.

[0058] Step Six: Based on the center frequency set, obtain its median value, and classify the mode functions with center frequencies greater than this median value into a high-frequency mode set. Superimpose the high-frequency mode sets to obtain the high-frequency reconstructed signal, such as... Figure 5 As shown, the specific expression is:

[0059] In the formula, x high ( t () is a high-frequency reconstructed signal. u k ( t ) is the first K One modal component.

[0060] Step 7: After obtaining the high-frequency reconstructed signal, perform energy analysis on both the signal and the original tangential grinding force signal to calculate their energy distribution over the entire time series. Determine the high-frequency energy ratio sequence by comparing the proportion of the high-frequency signal energy to the total energy of the original signal. The specific calculation steps are as follows: First, the total energy of the original tangential grinding force signal in the time domain is calculated to characterize the energy distribution of the entire signal over the time series. The calculation method is as follows:

[0061] In the formula, E total The total energy of the original signal. x ( t ) represents the original tangential force signal.

[0062] Secondly, the energy of the high-frequency reconstructed signal is calculated to characterize the energy distribution of the signal in the high-frequency subspace. The calculation method is as follows:

[0063] In the formula, x high ( t () is a high-frequency reconstructed signal.

[0064] Finally, to achieve time-series characterization of high-frequency energy, the local energy ratio is calculated using the sliding window method, resulting in a high-frequency energy ratio sequence:

[0065] In the formula, R ( i () indicates the center time of the window. i The high-frequency energy ratio at that location L The sliding window length controls the smoothness of the time-domain energy estimation; the numerator represents the time-domain integral of the high-frequency component energy within the window, and the denominator represents the time-domain integral of the total energy within the same window.

[0066] The peak point of the high-frequency energy ratio sequence is the critical time point for the elastic-plastic-brittle transition characteristics of metal materials during grinding. The grinding force corresponding to the critical time point is the critical grinding force for the elastic-plastic-brittle transition. Figure 6 As shown in the figure. Calculations show that the critical time point for the elastoplastic transition is 1.81 s, with critical normal and tangential grinding forces of 5.96 N and 1.35 N, respectively; the critical time point for the ductile-brittle transition is 3.34 s, with critical normal and tangential grinding forces of 12.47 N and 4.96 N, respectively; and the critical time point for complete brittleness is 4.14 s, with critical normal and tangential grinding forces of 15.93 N and 6.44 N, respectively.

[0067] like Figure 2 As shown, in specific implementation, according to step 1, the grinding force signal during the variable depth grinding process of titanium-aluminum alloy is collected, including the original tangential force signal and the original normal force signal.

[0068] like Figure 4 As shown, in specific implementation, according to step 5, the center frequencies of the five intrinsic mode functions are calculated as follows: IMF1=0.14HZ, IMF2=1.77HZ, IMF3=4.53HZ, IMF4=8.45HZ, and IMF5=15.37HZ.

[0069] In traditional methods of identifying the critical points of elastic, plastic, and brittle transitions in materials by directly observing surface morphology or analyzing raw grinding force signals, the complex post-grinding surface morphology, influenced by factors such as processing parameters, grinding wheel wear, and thermal effects, makes it difficult to accurately determine changes in the material's mechanical state based solely on visual observation or conventional testing methods. Furthermore, traditional signal processing methods have significant limitations when dealing with non-stationary and nonlinear signals, failing to effectively reflect the transient characteristics and time-frequency variations of grinding force signals, resulting in low accuracy in identifying the brittle-plastic transition point. However, the material removal critical grinding force calculation method based on a variational mode model proposed in this invention, by performing variational mode decomposition on the tangential grinding force signal, achieves multi-scale frequency separation and feature extraction of the signal, accurately identifying the critical point of transition from plastic cutting to brittle fracture in metallic materials during grinding, and calculating the corresponding critical normal and tangential grinding forces. By combining real-time monitoring and measurement results during actual processing, grinding using the plastic range determined by this invention can not only effectively reduce surface and surface layer damage and improve the surface quality and structural integrity of materials, but also optimize grinding parameter configuration, improve processing efficiency, and extend grinding wheel life, thereby significantly reducing manufacturing costs.

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the critical grinding force for material removal based on a variational modal model, characterized in that, Includes the following steps: Step 1: Collect grinding force signals during the metal variable cutting deep grinding process, extract the tangential grinding force signal from the grinding force signal, establish the original tangential grinding force data sample, and extract the time data and corresponding tangential grinding force data from the original tangential grinding force data sample; Step 2: Perform sampling interval detection on the extracted time data to determine the uniformity of the time interval. If it is uniform, establish equal sampling interval tangential grinding force data samples by combining the time data and the corresponding tangential grinding force data in the original tangential grinding force data sample. If the data is non-uniform, then construct equal-interval time data and perform linear interpolation resampling on the tangential grinding force data. Then, establish equal-sampling-interval tangential grinding force data samples by combining the equal-interval time data with the resampled tangential grinding force data. Step 3: Determine the parameters of the variational mode decomposition of the tangential grinding force by using tangential grinding force data samples with equal sampling intervals; Step 4: Introduce the determined variational mode decomposition parameters of the tangential grinding force into the variational mode model, use the variational mode model to decompose the tangential grinding force data samples with equal sampling intervals, obtain mutually independent intrinsic mode functions through iterative optimization, and save the mutually independent intrinsic mode functions in time series order to form a mode function sample set; Step 5: Perform frequency domain analysis on the independent intrinsic mode functions in the modal function sample set, calculate their spectrum function using fast Fourier transform, and construct the power spectral density function in the form of the square of the amplitude of the spectrum function. Based on the distribution of the power spectral density function, calculate the center frequency of the independent intrinsic mode function using the power weighted average method, and establish a center frequency set for each center frequency. Step 6: Based on the center frequency set, obtain the median value, and classify the eigenmode functions with center frequencies greater than the median value into the high-frequency mode set. Superimpose the high-frequency mode sets to obtain the high-frequency reconstructed signal. Step 7: After obtaining the high-frequency reconstructed signal, perform energy analysis on the high-frequency reconstructed signal and the original tangential grinding force data sample respectively, and calculate the energy distribution of the two in the entire time series; determine the energy ratio of the high-frequency reconstructed signal by comparing the proportion of the energy of the high-frequency reconstructed signal to the total energy of the original tangential grinding force data sample. The peak point of the high-frequency reconstructed signal energy ratio is the critical time point of the elastic-plastic-brittle transition characteristics of the metal material during grinding. The grinding force corresponding to the critical time point is the critical grinding force for the elastic-plastic-brittle transition.

2. The method for calculating the critical grinding force for material removal based on a variational mode model as described in claim 1, characterized in that, The grinding force signal collected in step one during the metal variable cutting deep grinding process is selected from the grinding force signal data obtained by a benchtop force gauge during the time period from 1 second after the grinding wheel enters the tool to 1 second before it retracts the tool, in order to ensure the stability of the data. The established original tangential grinding force data sample is obtained by extracting the tangential grinding force signal image from the overall grinding process monitoring data. This image serves as the original tangential grinding force data sample, from which time data and corresponding tangential grinding force data are extracted, as follows: ， ， In the formula, D This is a sample of the original tangential grinding force data. t i It is a time series. F i For the corresponding original tangential grinding force data, t For the extracted time data, x ( t ) represents the corresponding tangential grinding force data.

3. The method for calculating the critical grinding force for material removal based on a variational mode model as described in claim 1, characterized in that, The method for determining the uniformity of the time interval in step two, which involves sampling interval detection of the extracted time data, is expressed as follows: ， ， In the formula, Δ t For time step, median The median. std Standard deviation, mean The value is the average; if the condition is met, it indicates that the extracted time data is uniform; if the condition is not met, it indicates that the extracted time data is not uniform. If the extracted time data is uneven, the constructed equally spaced time data is as follows: ， In the formula, t j For data with equal time intervals, Δ t For time step; Then, linear interpolation resampling is performed on the tangential grinding force data to calculate the resampled tangential grinding force data corresponding to equal time intervals: ， ， In the formula, x k For tangential grinding force data, y j This is the resampled tangential grinding force data.

4. The method for calculating the critical grinding force for material removal based on a variational mode model as described in claim 1, characterized in that, The parameters for the variational modal decomposition of the tangential grinding force in step three include the penalty factor α, the quadratic penalty term τ, the number of decomposed modes K, and the DC component flag. DC The initialization method (init) and the convergence threshold (tol) are used; the selection rules for these parameters are as follows: The penalty factor α is used to control the modal bandwidth. Its value is determined based on the smoothness and noise level of the grinding signal. When the signal noise is large or the characteristic frequency band is wide, α takes a larger value (1000 - 5000) to enhance the smoothness of the components; when the signal fluctuation is small or the frequency band is narrow, α takes a smaller value (100 - 800) to preserve details. The quadratic penalty term τ is the time step of the Lagrange multiplier update, which is generally zero or a small positive number to ensure stable convergence of the algorithm. The number of decomposed modes K is determined based on the signal complexity and the number of main frequency bands, and is usually between 3 and 8. For grinding force signals, it is preferred to be 5 in order to balance modal resolution and computational complexity. DC component mark DC Determine whether to include a zero-frequency mode; set to 1 if the signal contains a stable baseline component, otherwise set to 0. The initialization method `init` indicates the initial center frequency setting method. It is preferable to use uniform distribution initialization with `init=1` to avoid getting trapped in local optima. The convergence threshold tol controls the decomposition accuracy, and its value ranges from 10. -5 -10 -8 Convergence is determined when the change in mode between adjacent iterations is less than this threshold.

5. The method for calculating the critical grinding force for material removal based on a variational mode model as described in claim 1, characterized in that, The expression for decomposing the tangential grinding force data samples with equal sampling intervals using the variational modal model in step four is as follows: ， In the formula, u k ( t ) is the first K One modal component, w k For the first K One central angular frequency, For the Dirac function, For convolution operators, For L2 norm operations, s . t . represents the constraint condition. y j For resampled tangential grinding force data; The iterative optimization obtained K The independent intrinsic mode functions are stored in time series order as IMF1, IMF2, ..., IMF K The modal function sample set is represented as follows: ， In the formula, IMF for K A number of independent eigenmode functions K It is a time series.

6. The method for calculating the critical grinding force for material removal based on a variational mode model as described in claim 1, characterized in that, The process of performing frequency domain analysis on the independent eigenmode functions in the modal function sample set and calculating their spectrum functions using Fast Fourier Transform in step five is as follows: ， In the formula, f For frequency variables, U k ( f ) is the first k The complex spectrum of each modal component u k ( t ) is the first K One modal component; The power spectral density function is constructed using the square of the amplitude of the spectral function. The process is as follows: ， In the formula, Pk ( f ) is the power spectral density function. Uk ( f ) represents the complex spectrum of the k-th modal component; Based on the distribution of the power spectral density function, the center frequencies of the independent eigenmode functions are calculated using the power-weighted average method. The process is as follows: ， In the formula, f c,k For the first k The center frequency of each mode; This represents summation over all frequency points; P k ( f ) is the power spectral density function.

7. The method for calculating the critical grinding force for material removal based on a variational mode model as described in claim 1, characterized in that, The high-frequency reconstruction signal in step six is: ， In the formula, xhigh ( t () is a high-frequency reconstructed signal. UK ( t ) is the first K One modal component.

8. The method for calculating the critical grinding force for material removal based on a variational mode model as described in any one of claims 1-7, characterized in that, The calculation of the high-frequency reconstructed signal energy ratio in step seven includes the following steps: First, the total energy of the original tangential grinding force data samples in the time domain is calculated to characterize the energy distribution of the entire signal over the time series. E total The calculation method is as follows: ， In the formula, x ( t This represents the original tangential grinding force signal; Secondly, the energy of the high-frequency reconstructed signal is calculated to characterize the energy distribution of the signal in the high-frequency subspace. The calculation method is as follows: ， In the formula, Ehigh The energy of the high-frequency reconstructed signal, xhigh ( t () is a high-frequency reconstructed signal; Finally, to achieve time-series characterization of high-frequency energy, the local energy ratio of the signal is calculated using the sliding window method to obtain the energy ratio of the high-frequency reconstructed signal: ， In the formula, R ( i () indicates the center time of the window. i The high-frequency energy ratio at that location L The sliding window length controls the smoothness of the time-domain energy estimation; the numerator represents the time-domain integral of the high-frequency component energy within the window, and the denominator represents the time-domain integral of the total energy within the same window.

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